TL;DR
This paper provides a self-contained proof demonstrating that acyclic and locally acyclic cluster algebras are equivalent to their upper cluster algebras, clarifying their structural relationship.
Contribution
It offers a new, self-contained proof establishing the equivalence of acyclic, locally acyclic, and upper cluster algebras.
Findings
Acyclic and locally acyclic cluster algebras coincide with their upper cluster algebras
The proof is self-contained and clarifies the structural relationship
Enhances understanding of cluster algebra classifications
Abstract
This note presents a self-contained proof that acyclic and locally acyclic cluster algebras coincide with their upper cluster algebras.
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